{"id":"https://openalex.org/W2073093064","doi":"https://doi.org/10.1137/100786800","title":"Domination Game and an Imagination Strategy","display_name":"Domination Game and an Imagination Strategy","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2073093064","doi":"https://doi.org/10.1137/100786800","mag":"2073093064"},"language":"en","primary_location":{"id":"doi:10.1137/100786800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786800","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089443562","display_name":"Bo\u0161tjan Bre\u0161ar","orcid":"https://orcid.org/0000-0001-8471-4796"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bo\u0161tjan Bre\u0161ar","raw_affiliation_strings":["bostjan.bresar@uni-mb.si#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bostjan.bresar@uni-mb.si#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049148828","display_name":"Sandi Klav\u017ear","orcid":"https://orcid.org/0000-0002-1556-4744"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sandi Klav\u017ear","raw_affiliation_strings":["sandi.klavzar@fmf.uni-lj.si#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"sandi.klavzar@fmf.uni-lj.si#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073086838","display_name":"Douglas F. Rall","orcid":"https://orcid.org/0000-0002-5482-756X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douglas F. Rall","raw_affiliation_strings":["doug.rall@furman.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"doug.rall@furman.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8708,"has_fulltext":false,"cited_by_count":169,"citation_normalized_percentile":{"value":0.90570093,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"24","issue":"3","first_page":"979","last_page":"991"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9656000137329102,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9532999992370605,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.825687050819397},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.8082585334777832},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7776896953582764},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7656776905059814},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7560217380523682},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7011376619338989},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6365013718605042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36849159002304077}],"concepts":[{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.825687050819397},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8082585334777832},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7776896953582764},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7656776905059814},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7560217380523682},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7011376619338989},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6365013718605042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36849159002304077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100786800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786800","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1504440667","https://openalex.org/W1583318653","https://openalex.org/W1989513471","https://openalex.org/W2015663147","https://openalex.org/W2053362603","https://openalex.org/W2055224148","https://openalex.org/W2059431770","https://openalex.org/W2076873334","https://openalex.org/W2076915992","https://openalex.org/W2086262777","https://openalex.org/W2094108224","https://openalex.org/W2105137385","https://openalex.org/W2107628600","https://openalex.org/W2110523058","https://openalex.org/W2144293155","https://openalex.org/W2172267233","https://openalex.org/W2285730933","https://openalex.org/W2295838866","https://openalex.org/W2994106552","https://openalex.org/W3022336920","https://openalex.org/W4237803824","https://openalex.org/W4241263391","https://openalex.org/W4246941747","https://openalex.org/W4251206977"],"related_works":["https://openalex.org/W2070745899","https://openalex.org/W2738565459","https://openalex.org/W1464226492","https://openalex.org/W3201378981","https://openalex.org/W2080000226","https://openalex.org/W2794522194","https://openalex.org/W1588305999","https://openalex.org/W2963404550","https://openalex.org/W2264220954","https://openalex.org/W1983442375"],"abstract_inverted_index":{"The":[0,64],"domination":[1,66,98,155],"game":[2,65,154],"played":[3],"on":[4,96,152],"a":[5,20,27,90,149],"graph":[6,46,105,122],"G":[7,23],"consists":[8],"of":[9,74,128,134,157],"two":[10],"players,":[11],"Dominator":[12,41,78],"and":[13,53,108,125,136,148,166],"Staller,":[14],"who":[15],"alternate":[16],"taking":[17],"turns":[18],"choosing":[19],"vertex":[21,28,38],"from":[22],"such":[24],"that":[25,102,109,119,126],"whenever":[26],"is":[29,39,71,87,117,146,162],"chosen":[30,76],"by":[31],"either":[32],"player,":[33],"at":[34],"least":[35],"one":[36],"additional":[37],"dominated.":[40],"wishes":[42,55],"to":[43,56],"dominate":[44],"the":[45,58,72,82,97,129,153],"in":[47],"as":[48,51,60,62,89],"few":[49],"steps":[50],"possible,":[52],"Staller":[54],"delay":[57],"process":[59],"much":[61],"possible.":[63],"number":[67,73,156],"$\\gamma_g(G)$":[68,135],"(resp.,":[69,79],"$\\gamma_g'(G)$)":[70],"vertices":[75],"when":[77],"Staller)":[80],"starts":[81],"game.":[83,99],"An":[84],"imagination":[85],"strategy":[86],"developed":[88],"general":[91],"tool":[92],"for":[93,103,120,131],"proving":[94],"results":[95],"We":[100],"show":[101],"any":[104,121],"G,":[106,123],"$\\gamma(G)\\leq\\gamma_g(G)\\leq2\\gamma(G)-1$,":[107],"all":[110],"possible":[111],"values":[112,133],"can":[113,138],"be":[114,139],"realized.":[115,140],"It":[116],"proved":[118],"$\\gamma_g(G)-1\\leq\\gamma'_g(G)\\leq\\gamma_g(G)+2$,":[124],"most":[127],"possibilities":[130],"mutual":[132],"$\\gamma_g'(G)$":[137],"A":[141],"connection":[142],"with":[143],"Vizing's":[144],"conjecture":[145],"established,":[147],"lower":[150],"bound":[151],"an":[158],"arbitrary":[159],"Cartesian":[160],"product":[161],"proved.":[163],"Several":[164],"problems":[165],"conjectures":[167],"are":[168],"also":[169],"stated.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}